Here, we present new results using a formulation situated on the middle ground
between standard effective field theory on one hand and non-perturbative
effects on the other: We extend effective field theory by applying
non-adiabatic quantum dynamics, foregoing the derivative expansion of quantum
corrections that is implicitly assumed when they are expressed in
higher-curvature form. Our formulation will therefore be sensitive to new (and
possibly non-local) corrections, while maintaining the crucial condition of
general covariance. The importance of control on general covariance has
recently been highlighted by the finding that most black-hole models or other
space-time descriptions proposed in the field of loop quantum gravity violate
covariance [1]}, [2]}, [3]}. (Models that do not
violate, but rather deform, covariance include those studied in
[4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}.)
One of these no-go theorems about covariance, derived in [2]}, relies
on the local nature of current models and could therefore be evaded by
constructing suitable non-local quantum corrections. The present paper can be
considered a first step in this direction, studying non-local quantum
corrections in spherically symmetric canonical quantum gravity.
